a significance test for the slope of a regression model

Review a significance test for the slope of a regression model for AP Statistics and try 1 free AP-style practice question. 18 questions on this topic in AP Statistics · Unit 9 · Inference for Quantitative Data: Slopes.

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Question 1

A sports scientist studies the relationship between the number of hours of weekly practice and competition score for a random sample of 16 gymnasts, intending to test whether there is a linear relationship between practice hours and score. Computer output from the least-squares regression is shown below.

Predictor	Coef	SE Coef
Constant	4.200	1.100
Practice hours	0.680	0.150

$s=1.850$ , R-sq $=64.0\%$

Assuming all conditions for inference are met, which of the following is an appropriate test statistic for testing $H_0: \beta_1=0$ versus $H_a: \beta_1 \neq 0$ ?

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Full practice for AP Statistics · Unit 9 · Inference for Quantitative Data: Slopes: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts

Part a1 / 1 pts

Point 1: Earned

94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts

Point 1: Earned

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."